Regularization of the Covariant Derivative on Curved Space by Finite Matrices

Details Regularization of the Covariant Derivative on Curved Space by Finite Matrices Regularization of the Covariant Derivative on Curved Space by Finite Matrices

2006-06-17

arxiv.org/abs/hep-th/0606163v1

Prog.Theor.Phys.115:1189-1209,2006

Physics

High Energy Physics

High Energy Physics - Theory

21pages, no figure, to appear in Prog. Theor. Phys

Scientific paper

10.1143/PTP.115.1189

In a previous paper [M.~Hanada, H.~Kawai and Y.~Kimura, Prog. Theor. Phys. 114 (2005), 1295] it is shown that a covariant derivative on any n-dimensional Riemannian manifold can be expressed in terms of a set of n matrices, and a new interpretation of IIB matrix model, in which the diffeomorphism, the local Lorentz symmetry and their higher spin analogues are embedded in the unitary symmetry, is proposed. In this article we investigate several coset manifolds in this formulation and show that on these backgrounds, it is possible to carry out calculations at the level of finite matrices by using the properties of the Lie algebras. We show how the local fields and the symmetries are embedded as components of matrices and how to extract the physical degrees of freedom satisfying the constraint proposed in the previous paper.

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